Passive concentration dynamics incorporated into the library IB2d, a two-dimensional implementation of the immersed boundary method

Matea Santiago; Nicholas A Battista; Laura A Miller; Shilpa Khatri

doi:10.1088/1748-3190/ac4afa

Passive concentration dynamics incorporated into the library IB2d, a two-dimensional implementation of the immersed boundary method

Bioinspir Biomim. 2022 Mar 10;17(3). doi: 10.1088/1748-3190/ac4afa.

Authors

Matea Santiago¹, Nicholas A Battista², Laura A Miller¹, Shilpa Khatri³

Affiliations

¹ Department of Mathematics, University of Arizona, PO Box 210089, Tucson, AZ 85721, United States of America.
² Department of Mathematics and Statistics, The College of New Jersey, 2000 Pennington Rd., Ewing, NJ 08628, United States of America.
³ Department of Applied Mathematics, University of California Merced, 5200 North Lake Rd., Merced, CA 95343, United States of America.

PMID: 35026749
DOI: 10.1088/1748-3190/ac4afa

Abstract

In this paper, we present an open-source software library that can be used to numerically simulate the advection and diffusion of a chemical concentration or heat density in a viscous fluid where a moving, elastic boundary drives the fluid and acts as a source or sink. The fully-coupled fluid-structure interaction problem of an elastic boundary in a viscous fluid is solved using Peskin's immersed boundary method. The addition or removal of the concentration or heat density from the boundary is solved using an immersed boundary-like approach in which the concentration is spread from the immersed boundary to the fluid using a regularized delta function. The concentration or density over time is then described by the advection-diffusion equation and numerically solved. This functionality has been added to our software library,IB2d, which provides an easy-to-use immersed boundary method in two dimensions with full implementations in MATLAB and Python. We provide four examples that illustrate the usefulness of the method. A simple rubber band that resists stretching and absorbs and releases a chemical concentration is simulated as a first example. Complete convergence results are presented for this benchmark case. Three more biological examples are presented: (1) an oscillating row of cylinders, representative of an idealized appendage used for filter-feeding or sniffing, (2) an oscillating plate in a background flow is considered to study the case of heat dissipation in a vibrating leaf, and (3) a simplified model of a pulsing soft coral where carbon dioxide is taken up and oxygen is released as a byproduct from the moving tentacles. This method is applicable to a broad range of problems in the life sciences, including chemical sensing by antennae, heat dissipation in plants and other structures, the advection-diffusion of morphogens during development, filter-feeding by marine organisms, and the release of waste products from organisms in flows.

Keywords: advection–diffusion; biofluids; biomechanics; fluid-structure interaction; immersed boundary method; mathematical biology.

Publication types

Research Support, Non-U.S. Gov't
Research Support, U.S. Gov't, Non-P.H.S.

MeSH terms

Computer Simulation
Software*